For 2 grand you should be enjoying a 780 ti. Get the i5 4670k, as it will perform almost exactly the same as the 4770k in games. You can also get away with 8gb RAM for gaming. Reinvest that money into a 780 ti and you'll see at least a 25% increase in frame rate, even with less memory.

4K gaming will overflow the 3GB VRAM on that 780TI. You're need dual 290x's or titan blacks to get between 30-60fps on max settings (but no AA). Related, please watch this video with benchmarks: https://www.youtube.com/watch?v=XA2pfk_L9dU

First year engineering is almost exactly the same for everyone no matter what discipline you go into. You don't have much of a choice for which classes and profs you get. Some are good, some are terrible. I can't speak for Carleton, but I've never felt that I was getting a second tier education with electrical engineering here. Hope you like math.